the majority of funding public universities receive is provided either by private donors or state/federal funding, not tuition. tuition rates (and other things like salary levels and raises) are either directly set by state legislatures or subject to approval by legislatures.
for example, at my school the operational budget for 2011 - 2012 is $900 million dollars, of which $275 million comes from tuition and fees. that's not counting the additional several hundred millions of dollars which come through outside grants and revenue projects.
to expand: in a free market tuition rates would be responsive to factors such as number of applicants, the tuition rates of other similar institutions, the economy in general, etc. - sadly that's just not the case.